Friday, June 28, 2019

Playful Math 129

From affinitynumerology?
Welcome to the 10000001st (binary) Playful Math Carnival (aka Math Teachers at Play). We often try to start these with some interesting facts about the number, and I was surprised to see many lists of 129 different this or that. Maybe because of the special properties of 129...

It's on the internet, must be true. Regardless, I'm hoping for some good creative, optimistic and inspirational ...ah... vibrations? ... below, so we'll roll with it.

129 is, of course, not prime (3x43, making it semiprime), and I got to wondering which 2 digit primes were and were not prime when you add 100. What's the longest string of primes you could make xx, 1xx, 2xx, ...? 129 is also, fabulously, the sum of the first 10 primes. Which other consecutive sums of the first n primes are prime? Is that common? Why do we only worry about even n?

129 is a Blum integer. People evidently used to think Blum primes were good seed for RSA moduli.

$$129 \to 1^2+2^2+9^2 = 86 \to 8^2+6^2 =100 \to 1^2+0^2+0^2 =1$$
This makes 129 a happy number. (That procedure either leads to 1, happily, or to an 8 number repeating cycle.

The place holder name for the undiscovered element 129 is unbiennium. I'm not sure why I was surprised to find out that there are names for those...

Shakespeare's Sonnet 129 has a bit that makes you think maybe it's mathematical...
Mad in pursuit and in possession so, 
Had, having, and in quest to have, extreme; 
A bliss in proof and proved, a very woe; 
Before, a joy proposed; behind, a dream. 
But it ends, "All this the world well knows; yet none knows well To shun the heaven that leads men to this hell." so I think it was probably another relationship saga.

On to the posts!

129 Antigone is large main-belt asteroid about 114 km in diameter.
Submissions and Shares

Karen Campe jumped in with the perfect starting post. It could have been the carnival post, I think! Summer Math Refreshments has links to online events, chats and includes puzzles.

Manan Shah, who hosted Issue 128, shared a post Summer Excursion #6, which has three playful activities linking words and numbers. See also his Primal Words, a completely new-to-me idea. A little bit crypto. Manan's current challenge is: Give me math words (lower case) except for "integral", "derivative", or "calculus" and I'll give you a score A. Your tasks? (1) Find words with A / word length >= 4 (2) Find A for the three excepted words"

Denise Gaskins, the originator of this here blog carnival, has a free summer service: 8 weeks of fun math activities. All by just an an email sign up. See more at her Playful Math Sampler.

Paula Beardell Krieg is really looking for a math summer. She designed a calculus beach towel, which you can buy, too!

Some of My Recent Favorites

James Propp on Mazes, Puzzles and Proofs. (He also hosted the June Carnival of Mathematics.) His posts are proper essays - always well written and intriguing.

Try the NY Times tile game.

Tina Cardone on crochet patterns.

Mike Lawler's Family Math dug into angles in Zometool polyhedra.

Sarah Carter's latest Naoki Inaba puzzle share. If by some chance you are unfamiliar with Sarah's Monday Must Reads, they are a great sampler of each weeks math twitter and chock full of math play.

Loved this mathy post for Pride Month.

A Lee Sallows Magic Pyramid puzzle.

Chase Orton's address on using play to heal a broken relationship with math.

Graphic essay on a Hilma Af Klimt exhibition. (She's in my #mathart category.)

And I'll throw in my post for World Tessellation Day, which comes every June!

Summer Foxtrot

Professionally Developed

Summer is, of course, when teachers dig deep and retrench and so often engage in self-professional development (when not off in formal PD). Dylan Kane has been doing deep thinking and reflecting on race and teaching. And Wendy Menard recommended this anti-racist reading list at the NY Times. Maybe Marian Small's post on building your mathematical confidence.

Sunil Singh's Math Recess book is having a slowchat this summer.  Can't get more playful than summer recess, right?

'Til 130

The numerology folks also seem to feel 129 is an "angel number," which tells you to look to put your talents to the services of others. Right now, there's no designated host for Carnival 130 - which usually means Denise will make sure it's hosted at her place. But maybe 129 is telling you that you should host? Contact Denise or I to make it happen. Writing these is always fun, and helps you realize how much good stuff teachers and math afficianados are putting out there.

The Hindenberg was airship LZ 129.
ps> So there's this from Archimedes' Lab... Napoleon & Hitler!

  • They were born 129 years apart;
  • They came into power 129 years apart;
  • They declared war on Russia 129 years apart;
  • They were both 129 cm tall;
  • They were defeated 129 years apart!

I only made up one of those.

Monday, June 17, 2019

World Tessellation Day 2019

4th annual World Tessellation Day. Begun in 2016 by Emily Grosvenor for M. C. Escher's birthday. (More of that story and Emily's book.) Don't think I'll get a chance to make a new tessellation for today, but here are some of my favorites from the past year. (Mine followed by the real treats from others.)

In Isometric

GeoGebra applet
GeoGebra applet

GeoGebra applet

GeoGebra applet


Not nearly everything you could see. Do you have a favorite - list it in the comments, please! If you have ideas for a GeoGebra applet, I'd love to hear it. 

To explore further, there's a tessellation page on this blog, or a tag on my tumblr, or GeoGebra books for (mostly) tile altering tessellations and Islamic Geometric Patterns.

And happy WTD. Go cover something with a finite set of shapes and no gaps or overlaps! Might need to work on a better slogan.